The runs test simplifies a time series to two values (e.g. positive and negative, but you can pick any suitble y, not just 0) and basically checks how long the series stays on one of the two values – or how many times it changes.
+ + + + − − − + + + − − + + + + + + − − − −
When the residuals are white noise, you'd expect to see the sign changing rapidly. If you have long runs of one kind, there's something wrong.
The name Tobit is a pun on both Tobin, their creator, and their similarities to probit models.
The Tobit model is distinct from the truncated regression model, which is in general different and requires a different estimator.
According to Wikipedia, a Tobit model is simply any of a class of regression models in which the observed range of the dependent variable is censored in some way. Because Tobin's method can be easily extended to handle truncated and other non-randomly selected samples, some authors adopt a broader definition of the tobit model that includes these cases.
I get the sense that this was the earliest censoring model. It is a multiple linear regression but with censored responses if it is above or below certain cutpoints.
Tobin's idea was to modify the likelihood function so that it reflects the unequal sampling probability for each observation depending on whether the latent dependent variable fell above or below the determined threshold.[5] For a sample that, as in Tobin's original case, was censored from below at zero, the sampling probability for each non-limit observation is simply height of the appropriate density function. For any limit observation, it is the cumulative distribution, i.e. the integral below zero of the appropriate density function. The tobit likelihood function thus is a mixture of densities and cumulative distribution functions.
Note that You don't need to know about biases to debias!
From www.greaterwrong.com/posts/rrjCeQLopeHXicAZ6/practical-debiasing, the following appear to be powerful general techniques:
More:
It's been shown you can avoid some biases by training:
I agree with Deaton and Cartwright that randomized trials are often overrated. There is a strange form of reasoning we often see in science, which is the idea that a chain of reasoning is as strong as its strongest link. The social science and medical research literature is full of papers in which a randomized experiment is performed, a statistically significant comparison is found, and then story time begins, and continues, and continues—as if the rigor from the randomized experiment somehow suffuses through the entire analysis.
— (??, ????)